Mendelian randomization an approach that uses measured variation in genes to determine the causal effect of exposure on outcomes (Davey Smith 2003). MR studies are not biased by reverse causality since genes are constant and not modified by disease edevlopment.
Obesity is a major driver of cardiometabolic disorders in the general population. It has immense clinical and economic consequences including cost of medication and absenteeism from work leading to great loss incurred by employers (Apovian et al). In the past decades the prevalence of hypertension has increased. Besides, its a major risk factor for cardiovascular diseases and occurs alongside other cardiovascular disease risk factors to cause disease.
The aim of this study was to conduct a systematic literature review and metanalyses of MR studies to determine the causal role of higher BMI on hypertension, systolic and diastolic blood pressure.
We searched Medline on OvidSP for Mendelian randomization studies using the query (search terms) on 30th November 2022.
Papers were eligible for inclusion if they reported estimates from MR analysis specifically of genetically predicted adulthood BMI on hypertension, systolic or diastolic blood pressure. We excluded reviews, letters, commentary, articles of opinion and papers looking at childhood BMI.
We extracted and entered the data in predefined tables. From each MR study we extracted: the first author name, year of publication, title of the study, total sample size including cases and controls for binary outcomes, the exposure name, the outcome name, the number of instruments variables, the source of these SNPs, the ancestry of the study population and the causal estimates including mean difference (MD), odds ratios, beta estimates with 95% confidence intervals and standard errors where applicable.
Figure 1: Flow chart of study selection
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## keep
dat1 <- read.csv("BMI_Hypertension_SBP_DBP_MRevidencecsv.txt",header = TRUE,sep = "\t")
#make a unique id without resultsid to takeup the y-axis
dat1$ID <- paste(dat1$author,dat1$pmid.y,dat1$year, sep = "_")
#scaling the odds ratio to sd scale
scale_or <- function(data, estimate, lowerbound, upperbound,
sd) {
data_modified <- data %>%
mutate(OR_LI = round(exp((((log(estimate)/log(10)) -
(1.96 * (((log(upperbound) - log(lowerbound))/(2 *
1.96))/sqrt(3)))) * sd) * log(10)),
digits = 2)) %>%
mutate(OR_UI = round(exp((((log(estimate)/log(10)) +
(1.96 * (((log(upperbound) - log(lowerbound))/(2 *
1.96))/sqrt(3)))) * sd) * log(10)),
2)) %>%
mutate(oddsratio = round(exp(((log(estimate)/log(10)) *
sd) * log(10)), 2))
return(data_modified)
}
duplicate_subset <- function(data, estimate, lowerbound,
upperbound, sd) {
data_duplicatedcolumns <- data %>%
mutate(OR_LI = lowerbound) %>%
mutate(OR_UI = upperbound) %>%
mutate(oddsratio = estimate)
return(data_duplicatedcolumns)
}
# Wes Spiller 2022 - calculate the confidence
# intervals given point estimates and pvalue only
CI_calc_lower <- function(est, p) {
z = -0.862 + sqrt(0.743 - 2.404 * log(p))
se = est/z
lower_interval = est - (1.96 * se)
return(lower_interval)
}
CI_calc_upper <- function(est, p) {
z = -0.862 + sqrt(0.743 - 2.404 * log(p))
se = est/z
upper_interval = est + (1.96 * se)
return(upper_interval)
}
## Frank Windmeijer convert that between scales
## Percentage change in DBP due to a 1% change in
## BMI. Calculate the CIs from the point estimate
## and standard errors point estimate in mm Hg
## percentage change * Mean DBP in UKBiobank
## (perc/100) * 81.80 CI= estimate+_margin_error
## margin of error at 95% = 1.96*se
pointestimate_calc <- function(est) {
dbp = 81.80
point_est <- (est/100) * dbp
return(point_est)
}
CI_calc_lower_se <- function(est, se) {
dbp =81.80
point_est <- (est/100) * dbp
margin_error <- 1.96 * se
lowerinterval <- point_est - margin_error
return(lowerinterval)
}
CI_calc_upper_se <- function(est, se) {
dbp =81.80
point_est <- (est/100) * dbp
margin_error <- 1.96 * se
upperinterval <- point_est + margin_error
return(upperinterval)
}
#Calculate the scaling factor
frank_calc_sd <- function() {
one_percmeanBMI = (1/100) * 27.3224
sd_BMI_UKB = 4.77
sd_at_1_per_of_BMI = one_percmeanBMI/sd_BMI_UKB
return(sd_at_1_per_of_BMI)
}
#make a forest plot using ggplotly
forest_plot <- function(dat1,x,y,xmin,xmax,
title = " ",xlab =" ", ylab = " ",method,xintercept){
plot <- dat1 %>%
ggplot(.)+
geom_segment(aes(x = {{x}}, y={{y}},yend={{y}},xend={{x}}))+
geom_point(aes(x = {{x}}, y={{y}},color = {{method}}))+
geom_errorbarh(aes(xmin={{xmin}},xmax={{xmax}},y={{y}},height = .2))+
labs(title=title, x=xlab, y =ylab ) +
geom_vline(xintercept=xintercept, color="red", linetype='dashed', alpha=.5)+
theme_classic()
return(plot)
}
## Metaanalysis
MR_metaanalysis <- function(dat, method, measure) {
dat$logor <- log(dat$oddsratio)
dat$SE <- (log(dat$OR_UI) - log(dat$OR_LI))/(2 *
qnorm(0.025))
mr_meta <- rma(yi = dat$logor, sei = dat$SE, method = method,
measure = measure)
return(mr_meta)
}
#Plot results of metanalysis
forest_plot_meta <- function(meta_res, dat, refline, xlab = " ") {
forest(meta_res, header = "Author_PMID_Year", pch = 16,
cex = 0.75, xlab = xlab, transf = exp, refline = refline,
slab = dat$ID, xlim = c(-16, 10), at = seq(-2,
3, by = 1), ilab = cbind(dat$samplesize,
dat$NO_ofIVs), ilab.xpos = c(-5, -1), order = "obs")
text(c(-5, -1), 10, c("Sample size", "No of IVs"),
cex = 0.75, font = 2)
text(-16, -1, pos = 4, cex = 0.75, bquote(paste("RE Model (Q = ",
.(formatC(meta_res$QE, digits = 2, format = "f")),
", df = ", .(meta_res$k - meta_res$p), ", p = ",
.(formatC(meta_res$QEp, digits = 2, format = "f")),
"; ", I^2, " = ", .(formatC(meta_res$I2, digits = 1,
format = "f")), "%)")))
}
# head(dat1) Hypertension, odds ratio
P1 <- dat1 %>%
arrange(ID) %>%
filter(effectsizetype_id == "ID1" & OUTCOMEID ==
"O1" & exposurenotes == "Adult" & outcomenotes !=
"Gestational hypertension" & outcomenotes !=
"Incident hypertension" & population == "EUR" &
AnalysisType == "Main" & EXPOSURE == "BMI")
# Subset1 consist of entries that need scaling
subset1 <- P1 %>%
filter(sd != 0)
# subset1 Subset2 consist of entries that need
# not scaling
subset2 <- P1 %>%
filter(sd == 0)
# subset2 Scaling
subset1 <- scale_or(data = subset1, estimate = subset1$effectsize,
lowerbound = subset1$lowerinterval, upperbound = subset1$upperinterval,
sd = subset1$sd)
subset2 <- duplicate_subset(data = subset2, estimate = subset2$effectsize,
lowerbound = subset2$lowerinterval, upperbound = subset2$upperinterval,
sd = subset2$sd)
# Combine the two subsets
Total <- rbind(subset1, subset2)
# Total
# Systolic blood pressure, Beta estimates
P2 <- dat1 %>%
arrange(ID) %>%
filter(effectsizetype_id == "ID4" & OUTCOMEID ==
"O2" & AnalysisType == "Main" & exposurenotes ==
"Adult" & EXPOSURE == "BMI")
# Calculate lower and upper intervals given a
# point estimate and a pvalue
Wes_2022 <- P2 %>%
filter(pmid.y == 35947639) %>%
mutate(lowerinterval = CI_calc_lower(effectsize,
pvalue)) %>%
mutate(upperinterval = CI_calc_upper(effectsize,
pvalue))
P2_less_Wes_2022 <- P2 %>%
filter(pmid.y != 35947639)
# row bind the two dataframes
P2 <- rbind(Wes_2022, P2_less_Wes_2022)
# subset the data P2 scale the Beta effect
# estimates in place
P2[P2$sd != 0, ]$effectsize = P2[P2$sd != 0, ]$effectsize *
P2[P2$sd != 0, ]$sd
P2[P2$sd != 0, ]$lowerinterval = P2[P2$sd != 0, ]$lowerinterval *
P2[P2$sd != 0, ]$sd
P2[P2$sd != 0, ]$upperinterval = P2[P2$sd != 0, ]$upperinterval *
P2[P2$sd != 0, ]$sd
# Diastolic blood pressure,Beta estimates
P3 <- dat1 %>%
arrange(ID) %>%
filter(effectsizetype_id == "ID4" & OUTCOMEID ==
"O3" & AnalysisType == "Main" & exposurenotes ==
"Adult" & EXPOSURE == "BMI")
# # Calculate lower and upper intervals given a
# point estimate and a se
scalingfactor = frank_calc_sd()
Frank_2018 <- P3 %>%
filter(pmid.y == 31708716) %>%
mutate(lowerinterval = CI_calc_lower(effectsize,
se)/scalingfactor) %>%
mutate(upperinterval = CI_calc_upper(effectsize,
se)/scalingfactor) %>%
mutate(effectsize = pointestimate_calc(effectsize)/scalingfactor)
P3_less_Frank_2018 <- P3 %>%
filter(pmid.y != 31708716)
# row bind the two dataframes
P3 <- rbind(Frank_2018, P3_less_Frank_2018)
# subset the data P3 scale the Beta effect
# estimates in place
P3[P3$sd != 0, ]$effectsize = P3[P3$sd != 0, ]$effectsize *
P3[P3$sd != 0, ]$sd
P3[P3$sd != 0, ]$lowerinterval = P3[P3$sd != 0, ]$lowerinterval *
P3[P3$sd != 0, ]$sd
P3[P3$sd != 0, ]$upperinterval = P3[P3$sd != 0, ]$upperinterval *
P3[P3$sd != 0, ]$sd
# Hypertension; risk difference
P4 <- dat1 %>%
arrange(ID) %>%
filter(effectsizetype_id == "ID5" & OUTCOMEID ==
"O1" & AnalysisType == "Main" & exposurenotes ==
"Adult" & EXPOSURE == "BMI")
# Results expressed as increase in unit BMI
# percentage point. Thus: multiply by sd and
# divide by 100
P4[P4$sd != 0, ]$effectsize = P4[P4$sd != 0, ]$effectsize *
P4[P4$sd != 0, ]$sd/100
P4[P4$sd != 0, ]$lowerinterval = P4[P4$sd != 0, ]$lowerinterval *
P4[P4$sd != 0, ]$sd/100
P4[P4$sd != 0, ]$upperinterval = P4[P4$sd != 0, ]$upperinterval *
P4[P4$sd != 0, ]$sd/100
# Diastolic blood pressure, risk difference
P5 <- dat1 %>%
arrange(ID) %>%
filter(effectsizetype_id == "ID5" & OUTCOMEID ==
"O3" & AnalysisType == "Main" & exposurenotes ==
"Adult" & EXPOSURE == "BMI")
# 1SD increase in BMI increases 0.145 SD of DBP.
# Thus:
P5[P5$sd != 0, ]$effectsize = P5[P5$sd != 0, ]$effectsize *
P5[P5$sd != 0, ]$sd
P5[P5$sd != 0, ]$lowerinterval = P5[P5$sd != 0, ]$lowerinterval *
P5[P5$sd != 0, ]$sd
P5[P5$sd != 0, ]$upperinterval = P5[P5$sd != 0, ]$upperinterval *
P5[P5$sd != 0, ]$sd
Genetically predicted BMI was associated with increased risk for hypertension. We excluded incident and gestational hypertension from the analysis and limited the analysis to European population only denoted by EUR.
Louise AC Millard paper reports their findings in terms of 1 SD higher BMI genetic risk score (SD increase in BMI allelic score equates to 0.64kg/m^2 increase in BMI). Original SD in the UKBiobank is 4.77kg/m^2. We scaled the estimates to 1 SD scale, 1 SD = (4.77/0.64 = 7.45).
Tove Fall 2013, we have included the prevalent hypertension as the main findings and not ever hypertension since it has a very small sample size, using 1 SNP at FTO locus (one unit increase in BMI(kg/m^2). The results are expressed in terms of per unit increase in BMI 1 kg/m^2. To convert the estimates to 1 SD scale, we converted the odds ratio to beta scaled that using 1 SD = 4.62 kg/m^2 and transformed back to odds ratio.
Sussana et al, Study using UKBiobank, to convert the estimates from per unit increase in BMI 1kg/m^2 to 1 SD scale, sd = 4.77kg/m^2.
To scale the odds ratio to uniform scale of 1 SD, we converted the ORs to beta estimates, scale the beta estimates and revert to odds ratio.
Figure 2: Forest plot showing results of genetically predicted BMI in relation to hypertension. The results are scaled to 1 SD increase of BMI. Analyses includes individuals of European ancestry only
What is the meaning of this plot?
Of the 7 studies that are reporting MR results of hypertension, the
evidence therefore shows that genetically predicted higher adulthood BMI
is associated with increased risk for hypertension as shown on
Figure 2.
This metaanalysis found consistent results of higher genetically predicted BMI and increased risk for hypertension Figure 7. Unlike Martin et al with inflated causal estimates the other papers are consistent even when with as low as 1 instrument; the case of Fall et al 2013.
Louise et al used BMI genetic allelic score which is an instrument of lifelong BMI (exposure) instead of BMI at a given age. However we converted the scale to SD to match the rest of the papers.
Genetically predicted BMI is associated with an increase in systolic
blood pressure.
Beta coefficient is the degree of change of an outcome variable for
every 1 unit change in the predictor/exposure variable. T-test assesses
whether beta is significantly different from zero.
Beta coefficient is positive, interpretation is that for every 1-unit
increase in the predictor variable, the outcome will increase by the
beta coefficient value. Beta coefficient is negative, interpretation is
that for every 1-unit increase in the predictor variable, the outcome
will decrease by the beta coefficient value.
Timpson et al adjusted for antihypertensive use by adding 10 mm Hg to SBP. Timpson et al reported the effect estimates as change in blood pressure in mm Hg per 10% increase in BMI. Transform the scale form 10% to per 1 SD increase in BMI(Kg/m2). i) Divide the average BMI in Danish population (Copenhagen) by 10. 2.Divide the output with 4.27 which is the SD of BMI in Danish population. Multiply the estimates and the intervals with 1 divided by the output step 2,(1/0.6135831).
Fall et al 2015, adjusted for hypertensive medication. Calculate the mean BMI across the studies included and multiply the estimates to convert it to per 1 SD of BMI (SD = 4.62Kg/m^2).
Giontella et al adjusted for medication using a stepped addition method where the additional value to scale estimate the BP correctly was based on number of medication taken ranging from 1 to 4 medications.(Malmo Diet and Cancer cohort). While in Malmo Preventive Project cohort, 15 and 10 mmHg was added to SBP and DBP to correct for antihypertensive treatment since number of medications was not available. Giontella et al, we selected the Malmo Diet and Cancer as our main results with sample size of about ~29k vs malmo preventive project ~9k. They have reported their results in terms of SD change in SBP per 1 SD change in BMI. To scale the estimates, multiply the change in SBP with SD in the general population (14.2mm Hg)
Spiller et al 2018, constructed instruments form GIANT consortium on
UKBiobank. They have constructed a weighted allelic score from the 96
SNPs and used this as a single strong instrument compared to using
individual SNPs. They were comparing use of MRGXE with IVW in the
presence of pleiotropy, MRGXE gives unbiased estimates. The limitation
is that this sensitivity analysis method is only applicable to when we
have access to individual level data.
Spiller et al 2022; They report the estimates and the P-values only. We
calculated the confidence intervals by first calculating the z, then
calculate the SE and finally calculate the CI at 95%. To scale both
results to per SD of BMI, we have multiplied the estimates and their
intervals by 4.77Kg/m^2; the SD of BMI in UKBiobank and SD of SBP (19.38
mm Hg) IN UKB .
Figure 3: Forest plot showing results of genetically predicted BMI in relation to Systolic blood pressure. The results are scaled to per 1 SD. Analyses includes individuals of European ancestry only
What do the results imply?
This plot shows results of effects of genetically predicted adulthood
BMI on systolic blood pressure. The beta coefficients are scaled to per
1 SD increase in BMI (Kg/m^2). There is clear evidence that for every
one SD increase in genetically predicted BMI (Kg/m^2) is associated with
an increase in systolic blood pressure. This implies that a reduction in
BMI potentially results to a reduction in systolic blood pressure. Wes
Spiller et al 2022, is slightly different from the rest of the values
since they are using MR-G estimation under no interaction with
unmeasured selection (MR-GENIUS) which relies upon analogous assumptions
to MR-GxE. The observed difference could arise from bias due to
violations arising from one or more unmeasured interactions.
Figure 4: Forest plot showing results of genetically predicted BMI in relation to Diastolic blood pressure. The results are scaled to per 1 SD. Analyses includes individuals of European ancestry only
What does this mean?
For every 1 SD increase in genetically predicted BMI (Kg/m^2) is
associated with DBP. This implies that lowering the BMI will lead to a
reduction in DBP.
Figure 5: Forest plot showing risk difference of genetically predicted BMI in relation to Hypertension. . Analyses includes individuals of European ancestry only
This figure 6 below shows that genetic predisposition to higher BMI is associated with a higher risk for higher DBP. These are results of a single paper and we will not proceed to perform a metaanalysis.
Figure 6: Forest plot showing risk difference of genetically predicted BMI in relation to Diastolic blood pressure. . Analyses includes individuals of European ancestry only
Notes from Carlos et al:
The table is correct, those are risk differences.
A (causal) Risk Difference of a unit increase in D is defined as:
E[Y(d+1)] - E[Y(d)] In linear models equals the Risk Difference of a one
unit increase in the treatment, that is: = E[Y(d+1)] - E[Y(d)] Formula
(1) is an identification result of traditional MR/IV. It says that is
identified by the ratio of two regression coefficients.
Here BMI is standardized, so the Risk Difference tells you how much a
one standard deviation increase in BMI increases the risk of DBP. All
variables are standardized, so for DBP we have the 1 standard deviation
increase in BMI increases 0.145 standard deviations of DBP.
We performed metaanalysis where the effect estimates measure had adequate number of studies more than 1 study. We can not perform metaanalysis of outcome DBP and hypertension where MR estimates reported as risk difference since it includes only one study.
We performed metaanalysis of studies reporting on risk for hypertension as a result of increased genetically preicted BMI. MR estimates reported as odds ratios. We have not performed metaanalysis with regards to SBP and DBP, It is not clear how to specify that measure within metafor package.
##
## Random-Effects Model (k = 8; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## 4.6088 -9.2175 -5.2175 -5.3257 -2.2175
##
## tau^2 (estimated amount of total heterogeneity): 0.0096 (SE = 0.0074)
## tau (square root of estimated tau^2 value): 0.0982
## I^2 (total heterogeneity / total variability): 79.09%
## H^2 (total variability / sampling variability): 4.78
##
## Test for Heterogeneity:
## Q(df = 7) = 40.4309, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.4893 0.0421 11.6103 <.0001 0.4067 0.5719 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## estimate ci.lb ci.ub
## tau^2 0.0096 0.0023 0.0606
## tau 0.0982 0.0476 0.2462
## I^2(%) 79.0889 47.0542 95.9653
## H^2 4.7822 1.8887 24.7853
Metaanalysis results show that genetically predicted higher BMI is associated with increased risk for hypertension (Figure 7). This is consistent across studies.
Figure 7: Metaanalysis results for genetically predicted BMI in relation to hypertension. The results are scaled to 1 SD increase of BMI.Analyses includes individuals of European ancestry only
##
## Random-Effects Model (k = 7; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## 6.3546 -12.7093 -8.7093 -9.1258 -4.7093
##
## tau^2 (estimated amount of total heterogeneity): 0.0047 (SE = 0.0046)
## tau (square root of estimated tau^2 value): 0.0686
## I^2 (total heterogeneity / total variability): 67.16%
## H^2 (total variability / sampling variability): 3.05
##
## Test for Heterogeneity:
## Q(df = 6) = 26.4602, p-val = 0.0002
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 0.4558 0.0343 13.2985 <.0001 0.3886 0.5229 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## estimate ci.lb ci.ub
## tau^2 0.0047 0.0007 0.0204
## tau 0.0686 0.0259 0.1429
## I^2(%) 67.1612 22.5240 89.8695
## H^2 3.0452 1.2907 9.8712
Metaanalysis results show that genetically predicted higher BMI is associated with increased risk for hypertension (Figure 7). This is consistent across studies.
Figure 8: Metaanalysis results for genetically predicted BMI in relation to hypertension. The results are scaled to 1 SD increase of BMI.Analyses includes individuals of European ancestry only
##
## Random-Effects Model (k = 8; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -13.6130 27.2260 31.2260 31.1179 34.2260
##
## tau^2 (estimated amount of total heterogeneity): 2.0168 (SE = 1.4396)
## tau (square root of estimated tau^2 value): 1.4201
## I^2 (total heterogeneity / total variability): 84.76%
## H^2 (total variability / sampling variability): 6.56
##
## Test for Heterogeneity:
## Q(df = 7) = 49.6315, p-val < .0001
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 2.8208 0.5850 4.8217 <.0001 1.6742 3.9674 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## estimate ci.lb ci.ub
## tau^2 2.0168 0.5655 11.4689
## tau 1.4201 0.7520 3.3866
## I^2(%) 84.7633 60.9370 96.9359
## H^2 6.5631 2.5600 32.6362
The metaanalysis shows that genetic predisposition to higher BMI is associated with higher systolic blood pressure. The results were consistent across the studies with 4 studies reporting slighlty smaller changes in SBP.
Figure 9: Metaanalysis results for genetically predicted BMI in relation to systolic blood pressure. The results are scaled to 1 SD increase of BMI. Analyses includes individuals of European ancestry only
##
## Random-Effects Model (k = 7; tau^2 estimator: REML)
##
## logLik deviance AIC BIC AICc
## -6.9443 13.8887 17.8887 17.4722 21.8887
##
## tau^2 (estimated amount of total heterogeneity): 0.2590 (SE = 0.3212)
## tau (square root of estimated tau^2 value): 0.5090
## I^2 (total heterogeneity / total variability): 51.59%
## H^2 (total variability / sampling variability): 2.07
##
## Test for Heterogeneity:
## Q(df = 6) = 13.2792, p-val = 0.0388
##
## Model Results:
##
## estimate se zval pval ci.lb ci.ub
## 1.9252 0.2897 6.6462 <.0001 1.3575 2.4930 ***
##
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## estimate ci.lb ci.ub
## tau^2 0.2590 0.0000 2.2521
## tau 0.5090 0.0000 1.5007
## I^2(%) 51.5893 0.0000 90.2578
## H^2 2.0657 1.0000 10.2647
The metaanalysis shows that genetic predisposition to higher BMI is
associated with higher diastolic blood pressure. The results were
consistent across the studies with 2 studies reporting slighlty smaller
changes in DBP.
Figure 10: Metaanalysis results for genetically predicted BMI in relation to diastolic blood pressure. The results are scaled to 1 SD increase of BMI. Analyses includes individuals of European ancestry only
The overall evidence shows that genetic predisposition to higher BMI is causal for an individual being at risk for hypertension or raised systolic and diastolic blood pressure. Thus efforts towards reducing the BMI will sequentially result to decreased hypertension burden globally.